Units, Dimensions & Measurements – NDA Physics PYQs

NDA 2025-II

Q. 1. One parsec in astronomical units (A.U.) is about

(a)  2 × 10³ A.U.

(b)  2 × 10⁴ A.U.

(c)  2 × 10⁵ A.U.

(d)  2 × 10⁶ A.U.

Answer: (c) 2 × 10⁵ A.U.

Explanation: One parsec is defined as the distance at which one astronomical unit (A.U.) subtends an angle of one arcsecond. One parsec is approximately 3.086 × 10¹³ km, which equals about 2 × 10⁵ A.U. The parsec is used for measuring stellar and galactic distances. Concept Tested: Parsec: definition and relation to astronomical units

Q. 2. The energy, E, of a photon can be expressed as E = hf where f is the frequency and h is Planck’s constant. The dimensions of h are the same as that of

(a)  linear momentum

(b)  angular momentum

(c)  displacement

(d)  torque

Answer: (b) angular momentum

Explanation: From E = hf: h = E / f = [M L² T⁻²] / [T⁻¹] = [M L² T⁻¹]. Angular momentum = moment of inertia × angular velocity = [M L²] × [T⁻¹] = [M L² T⁻¹]. Both h and angular momentum share identical dimensions. Linear momentum is [M L T⁻¹]. Torque is [M L² T⁻²]. Displacement is [L]. Concept Tested: Dimensional analysis of Planck’s constant: equivalence with angular momentum

NDA 2025-I

Q. 3. The universal constant of gravitation G has the unit

(a)  N

(b)  m/s

(c)  Joule

(d)  N·m²/kg²

Answer: (d) N·m²/kg²

Explanation: From G = F r² / (m₁ m₂): units of G = N × m² / kg² = N m² kg⁻². This is consistent with the dimensional formula [M⁻¹ L³ T⁻²]. Newton (N) is a force unit, m/s is speed, and joule is energy: none of these match the unit of G. Concept Tested: SI unit of universal gravitational constant G

Q. 4. Which one of the following is dimensionless quantity?

(a)  Stress

(b)  Strain

(c)  Pressure

(d)  Force

Answer: (b) Strain

Explanation: Strain = change in length ÷ original length. Both quantities have the same unit (length), so they cancel. Strain is therefore dimensionless: it has no units. Stress, pressure, and force all have physical dimensions and cannot be dimensionless. Concept Tested: Dimensionless quantities: strain as a ratio

NDA 2022-II

Q. 5. The commercial unit of electrical energy is kilowatt-hour (kWh), which is equal to

(a)  3.6 × 10⁶ J

(b)  3.6 × 10³ J

(c)  10³ J

(d)  1 J

Answer: (a) 3.6 × 10⁶ J

Explanation: 1 kWh = 1 kW × 1 hour = 1000 W × 3600 s = 3,600,000 J = 3.6 × 10⁶ J. This is a direct conversion using the definition of the watt (1 W = 1 J/s). Option (b) is 3.6 kJ, which is only 1 watt-hour, not 1 kilowatt-hour. Concept Tested: Conversion of kilowatt-hour (kWh) to joules

NDA 2022-I

Q. 6. Which one of the following correctly represents the SI unit of resistivity?

(a)  Ω

(b)  Ω/m

(c)  Ω cm

(d)  Ω m

Answer: (d) Ω m

Explanation: Resistivity (ρ) is defined by R = ρ L / A, where R is resistance, L is length, and A is cross-sectional area. Rearranging: ρ = R × A / L = Ω × m² / m = Ω m. Ω/m and Ω cm are dimensionally wrong for resistivity. Concept Tested: SI unit of resistivity: ohm-metre (Ω m)

Q. 7. What is the dimension of gravitational constant?

(a)  ML³T⁻²

(b)  M⁻¹L³T⁻²

(c)  M²L⁻²T⁻²

(d)  M²L⁻¹T⁻²

Answer: (b) M⁻¹L³T⁻²

Explanation: From Newton’s law of gravitation: F = G m₁ m₂ / r². Solving for G: G = F r² / (m₁ m₂) = [M L T⁻²] × [L²] / [M²] = [M⁻¹ L³ T⁻²]. The negative exponent of M reflects that G has an inverse relationship with mass. Concept Tested: Dimensional formula of gravitational constant G

NDA 2021-II

Q. 8. The unit of the ratio between thrust and impulse is same as that of

(a)  frequency

(b)  speed

(c)  wavelength

(d)  acceleration

Answer: (a) frequency

Explanation: Thrust is a force: [M L T⁻²]. Impulse = Force × Time: [M L T⁻¹]. Thrust ÷ Impulse = [M L T⁻²] ÷ [M L T⁻¹] = [T⁻¹]. The dimension [T⁻¹] is that of frequency. Speed is [L T⁻¹], wavelength is [L], and acceleration is [L T⁻²]: none match [T⁻¹]. Concept Tested: Dimensional analysis: ratio of thrust to impulse equals frequency

NDA 2021-I

Q. 9. Consider the following statements about Light year:

1.  Light year is a unit for measurement of very large distances.

2.  Light year is a unit for measurement of very large time intervals.

3.  Light year is a unit for measurement of intensity of light.

Which of the statements given above is/are correct?

(a)  1, 2 and 3

(b)  2 and 3 only

(c)  1 and 2 only

(d)  1 only

Answer: (d) 1 only

Explanation: Statement 1 is correct. A light year is a unit of distance: the distance light travels in one year. Statement 2 is wrong: light year is not a unit of time. Statement 3 is wrong: light year has nothing to do with intensity of light. Only Statement 1 is true. Concept Tested: Light year: distinguishing what it measures from common misconceptions

★ JOVIK Exam Insight Light year has now appeared in four NDA papers (2017-II, 2018-I, 2019-I, 2021-I). Statement-based formats add an extra layer: UPSC now tests whether you can correctly reject the false statements, not just recall the definition.

Q. 10. Which one of the following cannot be the unit of frequency of a sound wave?

(a)  dB

(b)  s⁻¹

(c)  Hz

(d)  min⁻¹

Answer: (a) dB

Explanation: The unit of frequency is Hertz (Hz), which equals s⁻¹ (inverse second). min⁻¹ is also a valid expression of frequency (cycles per minute). The decibel (dB) is a unit of sound intensity level: it measures loudness on a logarithmic scale. dB has no meaning as a unit of frequency. Concept Tested: Units of frequency: distinguishing Hz, s⁻¹, min⁻¹ from dB

NDA 2020-I & II

Q. 11. Which one of the following is NOT the unit of energy?

(a)  Joule

(b)  Watt-hr

(c)  Newton-metre

(d)  kg-metre/sec²

Answer: (d) kg-metre/sec²

Explanation: Joule is the SI unit of energy. Watt-hour is a valid energy unit (1 Wh = 3600 J). Newton-metre (N·m) equals one joule: it is also an energy unit. However, kg·m/s² is the unit of force (the Newton), not energy. Energy requires an extra dimension of length: kg·m²/s². Concept Tested: Identifying correct and incorrect units of energy

NDA 2019-II

Q. 12. A student measures certain lengths using a meter scale having least count equal to 1 mm. Which one of the following measurements is more precise?

(a)  0·50 mm

(b)  29·07 cm

(c)  0·925 m

(d)  910 mm

Answer: (d) 910 mm

Explanation: Precision depends on the least count of the instrument: here, 1 mm. A reading is most precise when it is expressed in the same unit as the least count with no ambiguity. 910 mm is expressed directly to the millimetre, matching the instrument resolution. 29·07 cm implies 0.1 mm resolution. 0·925 m implies 0.5 mm. 0·50 mm implies resolution finer than the instrument. Only 910 mm is fully consistent with a 1 mm least count. Concept Tested: Precision of measurement: least count and significant figures

NDA 2019-I

Q. 13. Light year is a unit of measurement of

(a)  very large distances

(b)  time interval in years

(c)  amount of light received on earth in a year

(d)  mass of atoms

Answer: (a) very large distances

Explanation: The light year measures distance: specifically, the distance light travels in one year in vacuum. It is used to express the vast distances between stars and galaxies. It is not a measure of time, light intensity, or atomic mass. Concept Tested: Light year: definition and what it measures

Q. 14. 1 dyne (a unit of force in CGS system) equals to

(a)  10³ g cm/s²

(b)  10⁻³ g cm/s²

(c)  10⁵ kg m/s²

(d)  10⁻⁵ kg m/s²

Answer: (d) 10⁻⁵ kg m/s²

Explanation: 1 dyne = 1 g cm s⁻². Converting: 1 g = 10⁻³ kg and 1 cm = 10⁻² m. So 1 dyne = 10⁻³ kg × 10⁻² m s⁻² = 10⁻⁵ kg m s⁻² = 10⁻⁵ N. One dyne is a very small force: one hundred-thousandth of a newton. Concept Tested: CGS to SI conversion: dyne to newton

NDA 2018-I

Q. 15. Which one of the following is the value of 1 kWh of energy converted into joules?

(a)  1.8 × 10⁶ J

(b)  3.6 × 10⁶ J

(c)  6.0 × 10⁶ J

(d)  7.2 × 10⁶ J

Answer: (b) 3.6 × 10⁶ J

Explanation: 1 kWh = 1 kW × 1 hour = 1000 W × 3600 s = 3,600,000 J = 3.6 × 10⁶ J. The conversion requires multiplying power in watts by time in seconds. 1 watt = 1 joule per second, so watts × seconds = joules. Concept Tested: Conversion of kilowatt-hour into joules

Q. 16. Light year is a unit for measurement of

(a)  age of universe

(b)  very small time intervals

(c)  very high temperature

(d)  very large distance

Answer: (d) very large distance

Explanation: A light year is a unit of very large distance. It is the distance light travels in one year: approximately 9.46 × 10¹² km. It is not a unit of time, temperature, or any other quantity. Concept Tested: Light year as a unit of very large distance

NDA 2017-II

Q. 17. The symbol of SI unit of inductance is H. It stands for?

(a)  Holm

(b)  Halogen

(c)  Henry

(d)  Hertz

Answer: (c) Henry

Explanation: The SI unit of inductance is the Henry (H), named after the American scientist Joseph Henry. It should not be confused with Hertz (Hz), which is the unit of frequency. Holm and Halogen are not SI units. Concept Tested: SI unit of inductance: the Henry

Q. 18. Light year is a measure of?

(a)  time

(b)  distance

(c)  total amount of light falling on the Earth in a year

(d)  average intensity of light falling on the Earth in a year

Answer: (b) distance

Explanation: A light year is the distance that light travels in one year in vacuum. It equals approximately 9.46 × 10¹² km. It is a unit of distance, not time. The word ‘year’ in the name refers to the travel time of light, not to the quantity being measured. Concept Tested: Light year as a unit of distance

★ JOVIK Exam Insight Light year is the most frequently tested concept in this chapter. NDA has repeated it in four papers: 2017-II, 2018-I, 2019-I, and 2021-I. The name contains ‘year’: a time word: which is the trap. Always remind yourself: light year = distance.

NDA 2017-I

Q. 19. Which one of the following physical quantities has the same unit as that of pressure?

(a)  Angular momentum

(b)  Stress

(c)  Strain

(d)  Work

Answer: (b) Stress

Explanation: Pressure = Force ÷ Area = [M L T⁻²] ÷ [L²] = [M L⁻¹ T⁻²]. Stress is also Force ÷ Area, so it shares exactly the same dimensions and SI unit (Pascal). Strain is a dimensionless ratio. Angular momentum has dimensions [M L² T⁻¹]. Work has dimensions [M L² T⁻²]. Concept Tested: Dimensional equivalence of stress and pressure

NDA 2016-II

Q. 20. Which one of the following statements is correct?

(a)  The measurement of mass taken by a spring weighing balance is correct at the place where the spring balance is calibrated for

(b)  The measurement of mass taken by a spring weighing balance is correct at all places

(c)  The measurement of mass taken by a spring weighing balance is correct at the places where the acceleration due to gravity is same with the place where the spring balance is calibrated for

(d)  A spring balance cannot be used to measure mass at any place

Answer: (c) The measurement of mass taken by a spring weighing balance is correct at the places where the acceleration due to gravity is same with the place where the spring balance is calibrated for

Explanation: A spring balance measures weight (W = mg), not mass directly. It is calibrated assuming a fixed value of g. At any location where g differs from the calibration value, the spring balance gives an incorrect reading. It gives accurate mass readings only where g is the same as at the place of calibration. Concept Tested: Limitation of spring balance: dependence on local gravitational acceleration

NDA 2016-I

Q. 21. The S.I. unit of acceleration is

(a)  ms⁻¹

(b)  ms⁻²

(c)  cms⁻²

(d)  kms⁻²

Answer: (b) ms⁻²

Explanation: Acceleration = change in velocity ÷ time = (m s⁻¹) ÷ s = m s⁻². The SI base unit of length is the metre (m), not the centimetre or kilometre. cms⁻² and kms⁻² are CGS or informal units, not SI. ms⁻¹ is the unit of velocity, not acceleration. Concept Tested: SI unit of acceleration

NDA 2015-II

Q. 22. Which one of the following is the SI unit of the thermal conductivity of a material?

(a)  Wm⁻¹K⁻¹

(b)  Wm/K

(c)  Wm⁻¹/K⁻¹

(d)  Js⁻¹m⁻¹K

Answer: (a) Wm⁻¹K⁻¹

Explanation: Thermal conductivity is defined as heat transferred per unit time, per unit area, per unit temperature gradient. Its SI unit is W m⁻¹ K⁻¹ (watts per metre per kelvin). Options (b) and (c) are dimensionally inconsistent notations. Option (d) mixes units incorrectly. Concept Tested: SI unit of thermal conductivity

Q. 23. In SI unit of force ‘Newton’ (N) is given by (where m stands for metre and s stands for second):

(a)  1 N = 1 kg/ms²

(b)  1 N = 1 kgm/s²

(c)  1 N = 1 kg s²/m

(d)  1 N = 1 kg m s²

Answer: (b) 1 N = 1 kgm/s²

Explanation: Newton’s second law gives Force = mass × acceleration. Acceleration has units m s⁻². Therefore 1 N = 1 kg × 1 m s⁻² = 1 kg m s⁻² = 1 kg m / s². Options (c) and (d) place s² in the numerator, which is dimensionally wrong for acceleration. Concept Tested: SI definition of the Newton (unit of force)

NDA 2015-I

Q. 24. Match List I with List II and select the correct answer using the code given below the Lists:

List I (Physical Quantity)	List II (Unit)
A.  Distance	1.  Mole
B.  Amount of material	2.  Coulomb
C.  Amount of electrical charge	3.  Light year
D.  Energy	4.  Watt hour

Code:

(a)  A-3, B-1, C-2, D-4

(b)  A-3, B-2, C-1, D-4

(c)  A-4, B-2, C-1, D-3

(d)  A-4, B-1, C-2, D-3

Answer: (a) A-3, B-1, C-2, D-4

Explanation: Distance is measured in light years (A-3). Amount of material is measured in moles (B-1). Amount of electrical charge is measured in coulombs (C-2). Energy can be measured in watt hours (D-4). The light year is a unit of distance, not time: a common NDA trap. Concept Tested: Matching physical quantities to their correct SI or practical units

NDA 2014-II

Q. 25. The dimension of ‘impulse’ is the same as that of

(a)  pressure

(b)  angular momentum

(c)  work

(d)  linear momentum

Answer: (d) linear momentum

Explanation: Impulse = Force × Time = [M L T⁻²] × [T] = [M L T⁻¹]. Linear momentum = mass × velocity = [M] × [L T⁻¹] = [M L T⁻¹]. Both share identical dimensions. This follows from the impulse-momentum theorem: impulse equals the change in linear momentum. Concept Tested: Dimensional equivalence of impulse and linear momentum

NDA 2011-II

Q. 26. Kilowatt-hour is the unit of

(a)  potential difference

(b)  electric power

(c)  electric energy

(d)  electric potential

Answer: (c) electric energy

Explanation: The kilowatt-hour (kWh) is the commercial unit of electrical energy. Power is measured in kilowatts (kW). Energy equals power multiplied by time. One kWh = 1 kW × 1 hour = 3.6 × 10⁶ J. It is not a unit of power, potential difference, or electric potential. Concept Tested: kWh as a unit of electrical energy

★ JOVIK Exam Insight NDA has tested the kWh concept in at least three papers (2011-II, 2018-I, 2022-II). Always remember: kWh measures energy, not power.

NDA 2010-I

Q. 27. Which one of the following pairs does not have the same dimension?

(a)  Potential energy and kinetic energy

(b)  Density and specific gravity

(c)  Focal length and height

(d)  Gravitational force and frictional force

Answer: (b) Density and specific gravity

Explanation: Potential energy and kinetic energy both have dimensions [M L² T⁻²]. Focal length and height are both lengths [L]. Gravitational and frictional forces are both forces [M L T⁻²]. Density has dimensions [M L⁻³]. Specific gravity is a dimensionless ratio: it has no dimensions. This pair does not share the same dimension. Concept Tested: Dimensional equivalence of pairs: density vs. specific gravity

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